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Theorem md1 113
Description: is the unit of (left side).
Assertion
Ref Expression
md1 (𝜑 ⧟ (⊥ ⅋ 𝜑))

Proof of Theorem md1
StepHypRef Expression
1 ax-init 7 . . . . . . 7 (~ 𝜑𝜑)
21ax-ibot 4 . . . . . 6 (⊥ ⅋ (~ 𝜑𝜑))
32mdcoi 12 . . . . 5 ((~ 𝜑𝜑) ⅋ ⊥)
43mdasi 14 . . . 4 (~ 𝜑 ⅋ (𝜑 ⅋ ⊥))
54mdcod 11 . . 3 (~ 𝜑 ⅋ (⊥ ⅋ 𝜑))
65dfli2i 66 . 2 (𝜑 ⊸ (⊥ ⅋ 𝜑))
7 ax-init 7 . . . . . 6 (~ (⊥ ⅋ 𝜑) ⅋ (⊥ ⅋ 𝜑))
87mdcod 11 . . . . 5 (~ (⊥ ⅋ 𝜑) ⅋ (𝜑 ⅋ ⊥))
98mdasri 17 . . . 4 ((~ (⊥ ⅋ 𝜑) ⅋ 𝜑) ⅋ ⊥)
109ebotr 19 . . 3 (~ (⊥ ⅋ 𝜑) ⅋ 𝜑)
1110dfli2i 66 . 2 ((⊥ ⅋ 𝜑) ⊸ 𝜑)
126, 11ilb 96 1 (𝜑 ⧟ (⊥ ⅋ 𝜑))
Colors of variables: wff var nilad
Syntax hints:  wbot 1  wmd 2  ~ wneg 3  wlb 55
This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-init 7  ax-mdco 8  ax-mdas 9  ax-iac 32  ax-eac1 33  ax-eac2 34
This theorem depends on definitions:  df-lb 56  df-li 62
This theorem is referenced by:  md2  114
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